Test

---

load("Tonga.RData")

Abstract

Coral reef fishes frequently show a high degree of structure in their distribution and abundance, but the variables that affect their spatial arrangement are inadequetely understood. This study sought to explain the spatial structure of coral reef fish communities in Tongatapu, the main island in the archipelago of the Kingdom Tonga. A subset of 60 sites exclusive to Tongatapu were extracted from data retrieved from PANGEA. The total species richness was 304 species, with site richness ranging from 38 to 103. The species explaining most of the variation between sites were Pomacentrus callainus, Pomacentrus imitator, Chrysiptera taupou, Chromis margaritifer, Chromis chrysura, and Amblyglyphidodon melanopterus, contributing above average to beta diversity. Variation in fish communities between sites was then compared to changes in environmental variables including wave energy, distance from the lagoon, distance to the market, distance to the village, distance to deep depths, distance to shallow depths, visibility, and rugosity with a R2_adj of 0.3604. Spatial linear trends, positive dbMEM spatial components, and negative scale dbMEM spatial components all significantly contributed to the variation. Variation of the community data was partitioned into an environmental component, a linear trend, a positive scale dbMEM spatial component, and a negative scale scale dbMEM spatial component, explaining 49.51% of the total variation. Local (temporal) contributions to beta diversity (LCBD indices) were found to be significant but explained minimal variation by regression against environmental variables

Introduction

When considering coral reef fish, influences on species distributions are ample. This ranges from biological factors such as competition, environmental factors such as temperature, or even historical factors such as disturbance events (Lecchini et al., 2003). Amid a worldwide biodiversity crisis, investigating complex interactions within marine ecosystems is crucial. One of the most common methods to understand community response to disturbances consists of computing beta diversity (Lamyet al, 2015). This can be done by assessing directional changes in species composition across a given environment. Particularly, the spatial beta diversity is studied to understand process that explain the spatial variation in community composition (Legendre & Gauthier, 2014).

Prior to 2016, the Kingdom of Tonga, a Polynesian country and archipelago, was data deficient. In 2016, a partnership was developed between the Tongan Ministry of Fisheries and James Cook University in Townsville, Australia with the aim of implementing a national coral monitoring project (Smallhorn-Westet al, 2020). This allowed data Tonga’s first national coral reef monitoring expedition, in which 375 sites were surveyed across the three main island groups, Tongatapu, Ha’apai and Vava’u, to describe broad trends in the status of the country’s coral reefs and reef fish fishery. The primary aim of this research was to determine the present ecological status of Tonga’s reef ecosystem and determine the appropriate management strategies (Smallhorn-Westet al, 2020). Moreover, socio-environmental variables were evaluated to highlight and mitigate potential threats to the islands. This uncovered an important degree of human pressure, particularly in the main island Tongatapu. This island presented high levels of over fishing, low coral cover, and high densities of Diadema sp. sea urchins. Likewise, additional studies have highlighted pronounced spatial heterogeneity due to the interacting effects of local environmental conditions (Adjeroudet al, 2012).

While it is clear that certain biological and environmental variables are affecting this community, further work is required to assess the generality of their influence on different fish species, at different scales, and also within the context of spatial structures. This report aims to highlight the drivers of beta diversity around Tongatapu. Specifically, to investigate the spatial structure of fish communities and to relate the spatial patterns to gradients in environmental variables.

Materials

Coral reef ecological surveys conducted in the Kingdom of Tonga from 2016-2018 were obtained from PANGAEA®. The dataset consisted of 375 sites surveyed across the Tongatapu, Ha’apai and Vava’u island groups. Data includes reef fish belt transects and benthic photo quadrats or point intercept data. In addition, the values of a range of socio-environmental predictor variables are also included in this data set. All surveys were conducted on SCUBA. Metadata on depth, location, transect length, width etc. are included in the data files as described in Smallhorn-Westet al, 2020.

The original dataset combines multiple projects with slight variation in methods (A1, Table 1). For consistency and simplicity, a subset of data was used including 60 sites within the Tongatapu island from the James Cook University National monitoring project. From September 14th to November 8th, 2018, abundances and length of fish were collected at the species level along four 30-m belt transects at all 60 sites between depths of 3 to 12m. Large mobile fish species were recorded within a 5m belt of each transect, while small site-attached reef species were recorded within a 2m belt. Abundances were converted to density (#/m) using the transects lengths and widths. Biomass was calculated using the length and abundance of reef fish following the published length-weight relationships for each species (www.fishbase.org).

Methods

Exploratory Analysis

The primary purpose of this report was to determine the variables responsible for differences in beta diversity across sites in Tongatapu. For this reason, a broad approach was used to identify patterns in community, environmental, and spatial composition.

In attempts to reduce complexity and asymmetry of the data, a subset of 30 sites were analyzed with species having a minimum of 5 observations. However, throughout analyses, the complete data set explained more variation with complex analyses, particularly for Distance-Based Moran’s Eigenvector Maps. For consistency the complete data set was used for all analyses.

Analyses were primarily completed using density for the species assemblages due to differences in transect sizes. Specifically, some of the “large mobile fish species” such as the Yellowfin Parrotfish, had large variations in lengths ranging from 3cm to 27cm. Exploration was also completed using biomass for the species assemblages. This can be interesting as larger individuals often have larger impact on the organization, function, and dynamics of communities than smaller ones (Legendre et al, 1997). However, published length-weight relationships are not always reliable depending on the measurement type. For example, differences in fork length vs. total length which were not specified in the dataset.

Data was transformed prior to multivariate analysis with the exploration of Box-Cox family transformations. This was done to reduce the skewness of the data distribution and preserve Euclidean distance, using a coefficient having the property of double-zero asymmetrical. The LCD function (Legendre and Borcard, 2017) find the best exponent to reach multivariate normality. As the community data violated the assumptions of the functions (n<p) and were heavily asymmetrical, different exponents of the Box–Cox series were explored manually. This was done with the use of PCA to determine the coefficient preserving the Euclidean distance which explained most variation. These analyses suggested data was best transformed using with exponent 1 (no transformation) followed by chord transformations.

To see all exploratory analyses, please view:

Cluster Analysis

Cluster analyses were conducted to recognize discontinuous subsets in the environment, particularly spatial. Hierarchical clustering was chosen over non-hierarchical clustering as no specific number of clusters was expected. Using hierarchical clustering allowed non-overlapping clusters to be produced. Cophenetic correlations were calculated to assure the clustering model retained most of the information contained in the dissimilarity matrix. Gower distances were calculated to confirm the best clustering model of the dissimilarity matrix. To identify interpretable clusters, fusion levels values, average silhouette methods, binary matrices, and multiscale bootstrapping resampling methods were used. Spatial plots of the clustering methods were also created to represent results of our spatially explicit data.

#Density per km
tonga.d<-cast(tonga, formula = site~species, sum, value = "density", fill = 0)
tonga.d<-column_to_rownames(tonga.d, var = "site")

#chord using library(vegan)
tonga.dc <- decostand(tonga.d, "nor")
tonga.dc.d <- dist(tonga.dc)  

Clustering Method Selection

## [1] 0.6347326
## [1] 0.7449925
## [1] 0.8240864
## [1] 0.7234474

# Gower (1983) distance
(gow.dist.single <- sum((tonga.dc.d - tonga.single.coph) ^ 2)) # 315.3156
## [1] 315.3156
(gow.dist.comp <- sum((tonga.dc.d - tonga.comp.coph) ^ 2)) #  104.5889
## [1] 104.5889
(gow.dist.UPGMA <- sum((tonga.dc.d - tonga.UPGMA.coph) ^ 2)) # 30.69564 
## [1] 30.69564
(gow.dist.ward <- sum((tonga.dc.d - tonga.ward.coph) ^ 2)) # 6431.152
## [1] 6431.152

The cophenetic correlations, shepard-like diagrams, and Gower distances suggest that Unweighted pair-group method using arithmetic averages (UPGMA) clustering methods are best. However, given our data and the purpose of our analyses, Ward methods may be favorable. The analyses will continue comparing and contrasting the two.

Interpretable Clusters

The graphs of the fusion level values seem to suggest 7 or 8 groups, and reaffirm are decision to continue to evaluate Ward clustering methods.

Next, we will compute and plot p-values for all clusters (edges) of the dendrogram via multiscale bootstrap resampling.

## Creating a temporary cluster...done:
## socket cluster with 7 nodes on host 'localhost'
## Multiscale bootstrap... Done.
## Creating a temporary cluster...done:
## socket cluster with 7 nodes on host 'localhost'
## Multiscale bootstrap... Done.

AU p-value (printed in red), the abbreviation of “approximately unbiased” p-value, are calculated by multiscale bootstrap resampling. BP value (printed in green) are “bootstrap probability” values, which are accurate than AU value as p-value. Based on these dendograms, five (UPGMA) to six (Ward) cluster have high AU values (e.g. 95%) and are strongly supported by data.

#For for Ward's minimum variance clustering
par(mfrow = c(1, 2))
Si <- numeric(nrow(tonga.d))
for (k in 2:(nrow(tonga.d) - 1))
{
  sil <- silhouette(cutree(tonga.ward, k = k), tonga.dc.d)
  Si[k] <- summary(sil)$avg.width
}
k.best <- which.max(Si)
plot(
  1:nrow(tonga.d),
  Si,
  type = "h",
  main = "Silhouette-optimal number of clusters (Ward)",
  xlab = "k (number of clusters)",
  ylab = "Average silhouette width"
)
axis(
  1,
  k.best,
  paste("optimum", k.best, sep = "\n"),
  col = "red",
  font = 2,
  col.axis = "red"
)
points(k.best,
       max(Si),
       pch = 16,
       col = "red",
       cex = 1.5
)
kt <- data.frame(k = 1:nrow(tonga.d), r = 0)
for (i in 2:(nrow(tonga.d) - 1)) 
{
  gr <- cutree(tonga.ward, i)
  distgr <- grpdist(gr)
  mt <- cor(tonga.dc.d, distgr, method = "pearson")
  kt[i, 2] <- mt
}
k.best <- which.max(kt$r)
plot(
  kt$k,
  kt$r,
  type = "h",
  main = "Matrix correlation-optimal number of clusters (Ward)",
  xlab = "k (number of clusters)",
  ylab = "Pearson's correlation"
)
axis(
  1,
  k.best,
  paste("optimum", k.best, sep = "\n"),
  col = "red",
  font = 2,
  col.axis = "red"
)
points(k.best,
       max(kt$r),
       pch = 16,
       col = "red",
       cex = 1.5)

Barplot showing the average silhouette widths (Rousseeuw quality index) (left) for k = 2 to 60 groups and the matrix correlations between the original dissimilarity matrix and binary matrices computed from the dendrogram cut at various levels (right).These suggest the optimal number of clustering to be between 13 to 14 for Ward clustering methods, and 16 or 12 for the UPGMA clustering. Based on these combination of these test, we believe there will be 8 to 10 interpretable clusters.

Cluster mapping

The selected cluster were plotted on the Tongutapu map to be used for comparison with spatial analyses, such as dbMEM and LCBD analysis. When comparing the results of the Ward and UPGMA clusters, slight variations are seen, with smaller groups seen with UPGMA compared to Ward.

Unconstrained Ordination

Community

Chord transformed community data was explored using Principal Component Analysis. Species with high contribution to the explained variation were determined. Broken stick models were used to determine the number of interpretable components. Biplots were created using the cleanplot() function. Scaling 1 was used to visualize the association among objects, with variables whose vectors exited the circle of equilibrium contributing more to the explained variation of the PC axes. The goodness function was used to identify that reached a cumulative R2 score of at least 0.4 on the represented axes. To explain or confirm differences between groups of sites, additional PCA biplots were constructed using previous Ward and UPGMA clustering. Here clusters of sites were identified by colour.

#Preparing the community matrices of abundance, density, and biomass for multivariate analysis using chord transformations
tonga.a<-cast(tonga, formula = site~species, sum, value = "abundance", fill = 0) #raw abundance
tonga.a<-column_to_rownames(tonga.a, var ="site")
tonga.ac <- decostand(tonga.a, "nor")
tonga.ac.d <- dist(tonga.ac)
tonga.ac.pca <- rda(tonga.ac)

tonga.d<-cast(tonga, formula = site~species, sum, value = "density", fill = 0) #Density per km
tonga.d<-column_to_rownames(tonga.d, var = "site")
tonga.dc <- decostand(tonga.d, "nor")
tonga.dc.d <- dist(tonga.dc)
tonga.dc.pca <- rda(tonga.dc)

tonga.bkm<-cast(tonga, formula = site~species, sum, value  = "biomass_1000mkg", fill = 0) #biomass
tonga.bkm<-column_to_rownames(tonga.bkm, var ="site")
tonga.bkmc <- decostand(tonga.bkm, "nor")
tonga.bkmc.d <- dist(tonga.bkmc)
tonga.bkmc.pca <- rda(tonga.bkmc)

#Comparing pca summaries for abundance, density, biomass
summary(tonga.ac.pca)
summary(tonga.dc.pca)
summary(tonga.bkmc.pca)

The PCA summaries suggest density explains slightly more variation (68.24%) than abundance (64.67%) or biomass (67.41%) when using the chord transformations. The broken stick models coupled with the summaries suggest that at least 3 of the PC axes should be visualized. For example, for density, the amount of variation explained by the 3rd axes (12.71%) is almost equally important as the first two axes (18.75% on PC1 and 17.21% for PC2). With the 4th PC explaining 7.3% of the variation, almost half of PC3, we are content with the first 3 axes. However, given the broken stick model, it could be interesting to run the PC axes through an NMDS. Given that density explains more variation on the first 3 axes (48.73% compared to 44.72% for biomass), we are more interested this measure for the PCA biplots, but both are compared.

The PCA biplots show that the following species explaining most of the variance in terms of density to be:

• PC1: Pomacentrus callainus , Pomacentrus imitator and Chrysiptera taupou
• PC2: Chromis margaritifer and Chromis chrysura
• PC3: Amblyglyphidodon melanopterus

However, when we look at biplots using biomass, we observe different species: Scarus rivulatus, Scarus flavipectoralis, and Ctenochaetus striatus. These species do not appear on the density biplots unless the cumulative R2 scores is set to 0.3.

When comparing density to abundance, we see differences due to sampling. This is clear when taking Scarus flavipectoralis, the yellow parrot fish, as an example. This fish is considered a large mobile species and was counted within a 5m belt. However, it’s recorded range size varies between 3cm to 27 cm, likely including juveniles. In addition, these juveniles have different behaviours and patterns and are often counted with high abundances (Overholtzer & Motta, 1999). The biplots help visualize this bias and suggest that the analyses should using density .

Overall, the amount of information lost when comparing PC1~PC2, to PC1~PC3 does not seem to be crucial.

The biplots highlight species which may be influencing the clusters. In addition we see clear groupings along the 2nd axis.

Environment

Three primary environmental groups of environmental variables were used for the analyses; general environmental variables, distances, and benthic cover (Table 1.). These environmental variables were analyzed as separate matrices, as combined matrices, and through variation partitioning. Ordination methods (PCA) were used to visualize the variability of the sites in terms of environmental variables. For this, environmental variables were standardized using the scale argument to become dimensionally heterogeneous. Multicollinearity was measured using variance inflation factor (VIF), with variables with VIF > 5 removed.

Environmental Variables	General_e1	Distances_e5	Benthic Cover_e7	e1.5	e1.5.7
Visibility	O			O	O
Depth	O			O	O
Wave Energy	O			O	O
Fishing Pressure	O			O	O
Slope	O			O	O
Rugosity	O			O	O
Distance to land		O		O	O
Distance to 10m		O		O	O
Distance to 20m		O		O	O
Distance to market		O		O	O
Distance to lagoon		O		O	O
Distance to village		O		O	O
Hard Corals			O		O
Fire Corals			O		O
Invertebrates			O		O
Soft Corals			O		O
Sponges			O		O
			O		O

For the full methods on environmental variables, see “Exploratory.R”. In addition, see markdown file on R. to see exploratory analyses hidden with include=FALSE.

#Multicolinearity Analysis using Kobe's VIF function
VIF_analysis(e1) #none over 5
VIF_analysis(e5) #none over 5
VIF_analysis(e7)
VIF_analysis(e7[,-1])#none over 5
e7<-e7[,-1] #new env matrix
VIF_analysis(e7)
VIF_analysis(e1.5) #market VIF > 5 
VIF_analysis(e1.5[-11])
e1.5<-e1.5[,-11] #new env matrix
VIF_analysis(e1.5.7) #market VIF > 5 
VIF_analysis(e1.5.7[,-14, -3])
VIF_analysis(dplyr::select(e1.5.7, -3, -14)) #remove algae and sst
e1.5.7<-dplyr::select(e1.5.7, -3, -14) #new env matrix
VIF_analysis(e1.5.7)

Following the VIF analyses, algae was removed from e7, market removed from e1.5 and algae and sst from e1.5.7 to reduce multicollinearity.

Constrained Ordination

Indirect gradient analyses were completed to explore the relationship between the community data and the environmental variables. Canonical redundancy analyses (RDA) were used to examine the effects of the environmental variables on the community. The ordiR2step() function from the vegan package was used to select environmental variables which significantly increases the model’s adjusted R2. The significance of each model and their canonical axes were tested using permutation test. A final environmental matrix was created using variables from the model with the highest Adjusted R2 and lowest AIC. Results of the ordination were displayed using the triplots() function. Additional triplots were constructed using previous Ward and UPGMA clustering with clusters of sites identified by colour.

#general env
mod.pc1.e1 <- lm(site.scores$PC1~., e1)
summary(mod.pc1.e1) #sst, rugosity
mod.pc2.e1 <- lm(site.scores$PC2~., e1)
summary(mod.pc2.e1) #sst

#distances
mod.pc1.e5 <- lm(site.scores$PC1~., e5)
summary(mod.pc1.e5) #20m, market, village
mod.pc2.e5 <- lm(site.scores$PC2~., e5)
summary(mod.pc2.e5) #20m, lagoon, village

#benthic cover
mod.pc1.e7 <- lm(site.scores$PC1~., e7)
summary(mod.pc1.e7) #invert
mod.pc2.e7 <- lm(site.scores$PC2~., e7)
summary(mod.pc2.e7) #none? 


#Stepwise selection 
#PC1
zero.pc1.e1<- lm(site.scores$PC1~1, e1)
mod.pc1.e1.red <- step(zero.pc1.e1, formula(mod.pc1.e1), direction="both")
summary(mod.pc1.e1.red) 
mod.pc1.e1.red$anova # AIC=-250.15 : PC1 ~ sst +  rugosity 
#PC2
zero.pc2.e1 <- lm(site.scores$PC2~1, e1)
mod.pc2.e1.red <- step(zero.pc2.e1, formula(mod.pc2.e1), direction="both")
summary(mod.pc2.e1.red)
# AIC=-254.87 : PC2 ~depth 

#PC1
zero.pc1.e5<- lm(site.scores$PC1~1, e5)
mod.pc1.e5.red <- step(zero.pc1.e5, formula(mod.pc1.e5), direction="both")
summary(mod.pc1.e5.red) #AIC=-261.39: PC1 ~ market + `20m` + village 
#PC2
zero.pc2.e5 <- lm(site.scores$PC2~1, e5)
mod.pc2.e5.red <- step(zero.pc2.e5, formula(mod.pc2.e5), direction="both")
summary(mod.pc2.e5.red) #AIC=-273.89: PC1 ~ `20m` + market + village + lagoon

#PC1
zero.pc1.e7<- lm(site.scores$PC1~1, e7)
mod.pc1.e7.red <- step(zero.pc1.e7, formula(mod.pc1.e7), direction="both")
summary(mod.pc1.e7.red) #AIC=-235.76 - PC1 ~ invert 
#PC2
zero.pc2.e7 <- lm(site.scores$PC2~1, e7)
mod.pc2.e7.red <- step(zero.pc2.e7, formula(mod.pc2.e7), direction="both")
summary(mod.pc2.e7.red) #AIC=-239.89 - site.scores$PC2 ~ hard + soft

rda.e1 <- rda(tonga.dc, e1)
anova(rda.e1) # e1 explains a significant proportion of the variance of Y. 
rda.e5 <- rda(tonga.dc, e5)
anova(rda.e5) # e5 explains a significant proportion of the variance of Y. 
rda.e7 <- rda(tonga.dc, e7)
anova(rda.e7) # e7 explains a significant proportion of the variance of Y. 
rda.e1.5 <- rda(tonga.dc, e1.5)
anova(rda.e1.5) # e1.5.7 explains a significant proportion of the variance of Y. 
rda.e1.5.7 <- rda(tonga.dc, e1.5.7)
anova(rda.e1.5.7) # e1.5.7 explains a significant proportion of the variance of Y. 

mod0.e1<-rda(tonga.dc~1, e1)
mod1.e1<-rda(tonga.dc~., e1)
step.e1<-ordiR2step(mod0.e1, mod1.e1)
e1.anova<-step.e1$anova

mod0.e5<-rda(tonga.dc~1, e5)
mod1.e5<-rda(tonga.dc~., e5)
step.e5<-ordiR2step(mod0.e5, mod1.e5)
e5.anova<-step.e5$anova 

mod0.e7<-rda(tonga.dc~1, e7)
mod1.e7<-rda(tonga.dc~., e7)
step.e7<-ordiR2step(mod0.e7, mod1.e7)
e7.anova<-step.e7$anova

mod0.e1.5<-rda(tonga.dc~1, e1.5)
mod1.e1.5<-rda(tonga.dc~., e1.5)
step.e1.5<-ordiR2step(mod0.e1.5, mod1.e1.5)
e15.anova<-step.e1.5$anova

mod0.e1.5.7<-rda(tonga.dc~1, e1.5.7)
mod1.e1.5.7<-rda(tonga.dc~., e1.5.7)
step.e1.5.7<-ordiR2step(mod0.e1.5.7, mod1.e1.5.7)
e157.anova<-step.e1.5.7$anova

RsquareAdj(rda.e1.5.7)$adj.r.squared 
## [1] 0.4091631
RsquareAdj(step.e1.5.7)$adj.r.squared 
## [1] 0.3908369

## -----------------------------------------------------------------------
## Site constraints (lc) selected. To obtain site scores that are weighted
## sums of species scores (default in vegan), argument site.sc must be set
## to wa.
## -----------------------------------------------------------------------
## 
## 
## No factor, hence levels cannot be plotted with symbols;
## 'plot.centr' is set to FALSE

## -----------------------------------------------------------------------
## Site constraints (lc) selected. To obtain site scores that are weighted
## sums of species scores (default in vegan), argument site.sc must be set
## to wa.
## -----------------------------------------------------------------------
## 
## 
## No factor, hence levels cannot be plotted with symbols;
## 'plot.centr' is set to FALSE

The ordiR2step() function selects the best model for the given environmental matrices, by comparing the full and reduced model. The criteria for including the variable is based on both significance of the newly selected variables, and the comparison of adjusted variation j) explained by the selected variables to R^2_adj explained by the global model (with all variables); if the new variable is not significant or the R^2_adj of the model including this new variable would exceed the R^2_adj of the global model, the selection will be stopped. Comparing the models suggest that using the environmental matrix with more variables (e1.5.7) explains most variation. In addition, analyses did not seem to suggest variance partitioning between different environmental matrices to increase the amount of variation explained in the community.

When comparing the final ordistep model to the full model:

rda(formula = tonga.dc ~ market + 20m + vis + village + rugosity + hard + lagoon + land + wave + fp + slope, data = e1.5.7) rda(formula = tonga.dc ~ vis + depth + wave + fp + slope + rugosity + land + 10m + 20m + market + lagoon + village + hard + fire + invert + soft + sponge, data = e1.5.7)

both are significant and the later explains more variation (full R^2_adj = 0.3925, step R^2_adj = 0.3604). However, the ordistep model has more significant axes (4) and a lower AIC value (full = -39.44, step = -42.05). Finally, the comparing the triplots of the two models, we do not see critical differences.

Spatial

Geographic position data (latitude and longitude) of each site were transformed to Cartesian coordinates using the “geoXY” function in the SoDA package to identify linear trends in community composition. Once identified, the linear spatial trends present in the response data were removed prior to spatial analysis with distance-based Moran’s Eigenvector Maps. Variance partitioning was used to quantify the relative effects of environmental and spatial variables in shaping the reef fish communities. Finally, as a complement to the spatial eigenfunction analyses, local contribution to beta diversity (LCBD) scores were generated for each sample and used to identify those samples where the assemblage composition differed significantly from that of the mean assemblage. LCBD scores were generated from the chord distance matrix using the “LCBD.comp” function in the adespatial package. Resulting p-values were adjusted using the Holm correction for multiple comparisons.

tonga.xy.c<-scale(tonga.xy, center = TRUE, scale = FALSE)
tonga.dc.det <- resid(lm(as.matrix(tonga.dc) ~ ., data = tonga.xy)) #detrend 
tonga.dc.D1 <- dist(tonga.dc.det) #turn detrend into distance
## Spatial data: linear trends
rda.xy <- rda(tonga.dc, tonga.xy)
RsquareAdj(rda.xy)
anova(rda.xy)
# 0.12 explained with linear coordinates, so the residuals contain...
var.res=1-0.1198403 #= 0.8801597
var.res #so, this is what's left to explain with (not linear coordinates)

The anova highlights the significant spatial linear trend seen in our data explaining around 12% of the variation. This suggest that the remaining 88% can be explained by the dbMEM analysis. We visualize the significant spatial linear trend using a cubic-trend surface analysis of the chord transformed Tonga data. The analysis shows four significant independent models. The first model explains around 11% of the explained variation, and seems to display the sites found in the center of the “bay” in the north of the island. The second model explains around 8% of the variation, and seems to represent the sites along the northern cost of the island. We note a large section that does not seem to be included in any of the 4 models, which seems to represent sites around islands in the north east.

s.value(tonga.xy, dbmem.red, method = "size",symbol = "circle")

source("final/functions/scalog.R")
scalog(tonga.dbmem.rda)

The eigenvector-based spatial analyses is applied to the detrended data, with 16 dbMEM eigenvectors with positive spatial correlation identified. Using forward selection, 8 of the dbMEMs are selected and show significant spatial patterns with a significant model and adjusted R2 of 0.1925. The scalogram shows the explained variance (unadjusted R2) of the detrended, chord transformed data explained by the 16 dbMEM eigenfunctions, with color-coded permutation test results.

These dbMEMs show different spatial patterns of faunal distribution, with dbMEM1, dbMEM3 and dbMEM4 describing broad-scale differences in terms of spatial organisation, dbMEM5, dbMEM7, dbMEM9, and dbMEM11 describing medium-scale differences, and dbMEM14 explaining differences at a finer-scale. The significance of the axes are tested with an anova with only the first axis showing significance. As the residuals of the first axis are normally distributed, the fitted site scores are regressed to the environmental data. The regression suggest that certain of the distance variables in from the environmental data are significant, notably distance to the market, 20m of depth, land, and village explain spatial variance. However, distance to the lagoon and the other environmental variables do not seem to be significant.

tonga.rda2.axis1.env <- lm(tonga.rda2.axes[ ,1] ~ ., data = tonga.env)
shapiro.test(resid(tonga.rda2.axis1.env)) #residuals are normal
summary(tonga.rda2.axis1.env)

pander(tonga.rda2.axis1.env, add.significance.stars = T)

Fitting linear model: tonga.rda2.axes[, 1] ~ .

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	0.103	0.05715	1.802	0.07784
market	-1.372e-05	2.46e-06	-5.578	1.097e-06	* * *
20m	4.091e-05	1.352e-05	3.026	0.003972	* *
vis	-0.0006947	0.001429	-0.4862	0.629
village	1.624e-05	3.515e-06	4.62	2.903e-05	* * *
rugosity	-0.01481	0.009588	-1.545	0.1289
hard	0.0002059	0.0006242	0.3299	0.7429
lagoon	3.887e-06	2.671e-06	1.455	0.1521
land	-2.598e-05	9.991e-06	-2.6	0.01235	*
wave	1.387e-05	3.527e-05	0.3932	0.6959
fp	0.0004989	0.0003507	1.423	0.1613
slope	0.006115	0.009707	0.63	0.5317

Given the positive MEMs only explain 0.34 of the total variation, the negative dbMEMs were tested as well. When using an alpha criterion of 0.05, no dbMEMS are selected during the forward selection. However, with an alpha criterion < 0.6, the forward selection identifies 9 dbMEM eigenvectors with negative spatial correlation. While these dbMEMs are not individually significant, the significant anova suggest they nevertheless explain an important part of the variation. This suggest that neighbouring sites are generally more different from each other than you would expect randomly. This could possibly be related to MPAs, reef crests, or potential land affecting the results.

Variation Partitioning

Variation partitioning analyses were completed to quantify the various unique and combined fractions of variation explained by several sources. This was done using our best-model selected environmental variables, dbMEMs, and linear spatial trends. When partioning variation between environmental data, broad scale positive dbMEMS, fine scale positive dbMems, and spatial linear trends, anovas for the unique fractions were not significant.However, when using positive dbMEMS and negative dbMEMS, variance was significantly partitioned.

Variation partitioning of the undetrended tonga reef fish data into an environmental component (X1), a linear trend (X2), a positive scale dbMEM spatial component (X3) and negative spatial scale dbMEM spatial component (X4). The empty fractions in the plots have small negative R2_adj values. Together, 49.51% of the variation is explained, with a 10% increase when considering spatial variables.

Beta Diversity

Replacement, richness and nestedness indices of the fish data

When comparing presence absence data to quantitative data we get:

	BD Total	Replacement	Richness Difference	Repl/TotalB	RichDif/TotalB
quantitative	0.4169903	0.2717076	0.1452827	0.6515920	0.3484080
presence/ absence	0.34162115	0.26216129	0.07945986	0.76740358	0.23259642

Triangle plots of all pairs of sites in the Tonga data set, based on the Podani indices of richness or abundance difference, replacement, and corresponding similarities. In each plot, the mean values of the indices, as well as the position of a “mean pair of sites”, are represented by larger black dots. Species replacement is also called turnover when analysed along spatial or environmental gradients. The results of the plots may suggest that the simultaneous gain and loss of species due to environmental filtering/competition is occuring (Legendre, 2014).

# Display values of the mean points in the triangular plots
colMeans(fish.pod.J.3[, c(3, 1, 2)])
##   RichDiff Similarity       Repl 
##  0.1589197  0.3167577  0.5243226
colMeans(fish.pod.S.3[, c(3, 1, 2)])
##   RichDiff Similarity       Repl 
##  0.1227849  0.4752054  0.4020096
colMeans(fish.pod.qJ.3[, c(3, 1, 2)])
##     AbDiff Similarity       Repl 
##  0.2905655  0.1660194  0.5434151
colMeans(fish.pod.qS.3[, c(3, 1, 2)])
##     AbDiff Similarity       Repl 
##  0.2550097  0.2725305  0.4724599

Although both ANOVAs are significant, both the replacement (R^2_adj 0.0144) and the richness difference (R^2_adj 0.07098) show very weak relationships of the replacement/richness matrix with the environmental variables. This may be do to the very asymmetric community data or lack of appropriate environmental variables. Alternatively, the results may be explained by strong relationships to spatial and temporal variables which were not considered.

Species with SCBD larger than mean SCBD: - Scarus flavipectoralis 0.6365 - Chromis chrysura 0.0689 - Chromis viridis 0.05789 - Pomacentrus callainus 0.1149 - Chrysiptera taupou 0.1039 - Chromis chrysura 0.7198 –> Pomacentrus callainus, Chrysiptera taupou, Chromis chrysura, Amblyglyphidodon melanopterus, and Chromis chrysura explained most of the variation in the PCA biplots.

Sites with significant holm-correlated LCBD values: EFH1 (Euiki FHR), HkM2 (Hakau Manu 2), LgE2 (Lagoon Entrance 2)

Large LCBD values indicate sites that have strongly different species compositions compared with a mean site. The three significant sites may have unusual species combinations and high conservation value or degraded and species-poor sites that are good candidates for ecological restoration (Legendre and Gauthier, 2014).

Conclusion

This study attempted to determine the drivers of beta diversity of reef fish communities of Tongatapu island. The species explaining most of the variation between sites were all members of the Damselfish family. Studies suggest that damselfish have (Ceccarelli et al, 2001) a major influence on the structure of algal, coral, other invertebrate and fish assemblages on coral reefs. Discrepancies were found in analyses when using different abundance measurements. Specifically, juvenile fish likely influenced patterns seen using raw abundance and biomass. Distances to the market, the village, and the lagoon all explained variation in the community and may be represent human pressure. In fact, Land-based pollution from agricultural runoff and illegal dumping of waste are concern for lagoonal areas of Tongatapu. Conservation efforts should further investigate species with large SCBD and and sites with large LCBD values as they may indicate flourishing areas or areas in need of conservation (Legendre and Gauthier, 2014). Given that the replacement and richness differences were not explained by environmental variables, it is possible that they might be explained by spatial variables. In addition, temporal variables were not considered in the study. This is particularly important considering reef fish as they follow diurnal temporal variations patterns (Adjerou et al, 2012). As sampling hours varied between 9:00AM and 3:00PM between sites, this could have explained part of the variation. In addition, some of the sites are found in Special Management Areas, or Fish Habitat Reserves which may explain additional variation (see map below). Finally, in addition to taxonomic diversity, both functional diversity and phylogenetic diversity should be considered (Rozanski et al., 2022). The functional trait matrices and phylogenetic trees were prepared and are available but no analyses were included in the report. Moreover, the use of three diversity facets—richness, divergence, and regularity– can provide additional patterns for functional and phylogenetic biodiversity (Rozanski et al, 2022). For a comprehensive analysis, these three facets should be documented at alpha (within site), beta (between sites), and gamma (total diversity) biodiversity levels (Tucker et al., 2017)

References

sapply(my_libraries, citation)
## $tidyverse
## 
## To cite package 'tidyverse' in publications use:
## 
##   Wickham H, Averick M, Bryan J, Chang W, McGowan LD, François R,
##   Grolemund G, Hayes A, Henry L, Hester J, Kuhn M, Pedersen TL, Miller
##   E, Bache SM, Müller K, Ooms J, Robinson D, Seidel DP, Spinu V,
##   Takahashi K, Vaughan D, Wilke C, Woo K, Yutani H (2019). "Welcome to
##   the tidyverse." _Journal of Open Source Software_, *4*(43), 1686.
##   doi:10.21105/joss.01686 <https://doi.org/10.21105/joss.01686>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {Welcome to the {tidyverse}},
##     author = {Hadley Wickham and Mara Averick and Jennifer Bryan and Winston Chang and Lucy D'Agostino McGowan and Romain François and Garrett Grolemund and Alex Hayes and Lionel Henry and Jim Hester and Max Kuhn and Thomas Lin Pedersen and Evan Miller and Stephan Milton Bache and Kirill Müller and Jeroen Ooms and David Robinson and Dana Paige Seidel and Vitalie Spinu and Kohske Takahashi and Davis Vaughan and Claus Wilke and Kara Woo and Hiroaki Yutani},
##     year = {2019},
##     journal = {Journal of Open Source Software},
##     volume = {4},
##     number = {43},
##     pages = {1686},
##     doi = {10.21105/joss.01686},
##   }
## 
## 
## $skimr
## 
## To cite package 'skimr' in publications use:
## 
##   Waring E, Quinn M, McNamara A, Arino de la Rubia E, Zhu H, Ellis S
##   (2022). _skimr: Compact and Flexible Summaries of Data_. R package
##   version 2.1.4, <https://CRAN.R-project.org/package=skimr>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {skimr: Compact and Flexible Summaries of Data},
##     author = {Elin Waring and Michael Quinn and Amelia McNamara and Eduardo {Arino de la Rubia} and Hao Zhu and Shannon Ellis},
##     year = {2022},
##     note = {R package version 2.1.4},
##     url = {https://CRAN.R-project.org/package=skimr},
##   }
## 
## 
## 
## 
## $sf
## 
## To cite package sf in publications, please use:
## 
##   Pebesma, E., 2018. Simple Features for R: Standardized Support for
##   Spatial Vector Data. The R Journal 10 (1), 439-446,
##   https://doi.org/10.32614/RJ-2018-009
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     author = {Edzer Pebesma},
##     title = {{Simple Features for R: Standardized Support for Spatial Vector Data}},
##     year = {2018},
##     journal = {{The R Journal}},
##     doi = {10.32614/RJ-2018-009},
##     url = {https://doi.org/10.32614/RJ-2018-009},
##     pages = {439--446},
##     volume = {10},
##     number = {1},
##   }
## 
## 
## $readxl
## 
## To cite package 'readxl' in publications use:
## 
##   Wickham H, Bryan J (2022). _readxl: Read Excel Files_. R package
##   version 1.4.1, <https://CRAN.R-project.org/package=readxl>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {readxl: Read Excel Files},
##     author = {Hadley Wickham and Jennifer Bryan},
##     year = {2022},
##     note = {R package version 1.4.1},
##     url = {https://CRAN.R-project.org/package=readxl},
##   }
## 
## 
## 
## 
## $kableExtra
## 
## To cite package 'kableExtra' in publications use:
## 
##   Zhu H (2021). _kableExtra: Construct Complex Table with 'kable' and
##   Pipe Syntax_. R package version 1.3.4,
##   <https://CRAN.R-project.org/package=kableExtra>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {kableExtra: Construct Complex Table with 'kable' and Pipe Syntax},
##     author = {Hao Zhu},
##     year = {2021},
##     note = {R package version 1.3.4},
##     url = {https://CRAN.R-project.org/package=kableExtra},
##   }
## 
## 
## 
## 
## $vegclust
## 
## To cite 'vegclust' package in publications use:
## 
##   De Caceres, M., Font, X., Oliva, F. (2010). The management of
##   vegetation classifications with fuzzy clustering. Journal of
##   Vegetation Science 21: 1138-1151
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {The management of vegetation classifications with fuzzy clustering},
##     author = {Miquel {De Caceres} and Xavier Font and Francesc Oliva},
##     journal = {Journal of Vegetation Science},
##     year = {2010},
##     volume = {21},
##     pages = {1138-1151},
##     doi = {10.1111/j.1654-1103.2010.01211.x},
##   }
## 
## Thank you for using 'vegclust'
## 
## 
## $lubridate
## 
## To cite lubridate in publications use:
## 
##   Garrett Grolemund, Hadley Wickham (2011). Dates and Times Made Easy
##   with lubridate. Journal of Statistical Software, 40(3), 1-25. URL
##   https://www.jstatsoft.org/v40/i03/.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {Dates and Times Made Easy with {lubridate}},
##     author = {Garrett Grolemund and Hadley Wickham},
##     journal = {Journal of Statistical Software},
##     year = {2011},
##     volume = {40},
##     number = {3},
##     pages = {1--25},
##     url = {https://www.jstatsoft.org/v40/i03/},
##   }
## 
## 
## $janitor
## 
## To cite package 'janitor' in publications use:
## 
##   Firke S (2021). _janitor: Simple Tools for Examining and Cleaning
##   Dirty Data_. R package version 2.1.0,
##   <https://CRAN.R-project.org/package=janitor>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {janitor: Simple Tools for Examining and Cleaning Dirty Data},
##     author = {Sam Firke},
##     year = {2021},
##     note = {R package version 2.1.0},
##     url = {https://CRAN.R-project.org/package=janitor},
##   }
## 
## 
## 
## 
## $caper
## 
## To cite package 'caper' in publications use:
## 
##   Orme D, Freckleton R, Thomas G, Petzoldt T, Fritz S, Isaac N, Pearse
##   W (2018). _caper: Comparative Analyses of Phylogenetics and Evolution
##   in R_. R package version 1.0.1,
##   <https://CRAN.R-project.org/package=caper>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {caper: Comparative Analyses of Phylogenetics and Evolution in R},
##     author = {David Orme and Rob Freckleton and Gavin Thomas and Thomas Petzoldt and Susanne Fritz and Nick Isaac and Will Pearse},
##     year = {2018},
##     note = {R package version 1.0.1},
##     url = {https://CRAN.R-project.org/package=caper},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
## 
## 
## 
## 
## $RCurl
## 
## To cite package 'RCurl' in publications use:
## 
##   Temple Lang D (2022). _RCurl: General Network (HTTP/FTP/...) Client
##   Interface for R_. R package version 1.98-1.8,
##   <https://CRAN.R-project.org/package=RCurl>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {RCurl: General Network (HTTP/FTP/...) Client Interface for R},
##     author = {Duncan {Temple Lang}},
##     year = {2022},
##     note = {R package version 1.98-1.8},
##     url = {https://CRAN.R-project.org/package=RCurl},
##   }
## 
## 
## 
## 
## $XML
## 
## To cite package 'XML' in publications use:
## 
##   Temple Lang D (2022). _XML: Tools for Parsing and Generating XML
##   Within R and S-Plus_. R package version 3.99-0.10,
##   <https://CRAN.R-project.org/package=XML>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {XML: Tools for Parsing and Generating XML Within R and S-Plus},
##     author = {Duncan {Temple Lang}},
##     year = {2022},
##     note = {R package version 3.99-0.10},
##     url = {https://CRAN.R-project.org/package=XML},
##   }
## 
## 
## 
## 
## $dplyr
## 
## To cite package 'dplyr' in publications use:
## 
##   Wickham H, François R, Henry L, Müller K (2022). _dplyr: A Grammar of
##   Data Manipulation_. R package version 1.0.10,
##   <https://CRAN.R-project.org/package=dplyr>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {dplyr: A Grammar of Data Manipulation},
##     author = {Hadley Wickham and Romain François and Lionel Henry and Kirill Müller},
##     year = {2022},
##     note = {R package version 1.0.10},
##     url = {https://CRAN.R-project.org/package=dplyr},
##   }
## 
## 
## 
## 
## $reshape
## 
## To cite reshape in publications, please use:
## 
##   H. Wickham. Reshaping data with the reshape package. Journal of
##   Statistical Software, 21(12), 2007.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     author = {Hadley Wickham},
##     journal = {Journal of Statistical Software},
##     number = {12},
##     title = {Reshaping data with the reshape package},
##     url = {https://www.jstatsoft.org/v21/i12/},
##     volume = {21},
##     year = {2007},
##   }
## 
## 
## $writexl
## 
## To cite package 'writexl' in publications use:
## 
##   Ooms J (2021). _writexl: Export Data Frames to Excel 'xlsx' Format_.
##   R package version 1.4.0,
##   <https://CRAN.R-project.org/package=writexl>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {writexl: Export Data Frames to Excel 'xlsx' Format},
##     author = {Jeroen Ooms},
##     year = {2021},
##     note = {R package version 1.4.0},
##     url = {https://CRAN.R-project.org/package=writexl},
##   }
## 
## 
## 
## 
## $adespatial
## 
## To cite adespatial in publications use:
## 
##   Dray S, Bauman D, Blanchet G, Borcard D, Clappe S, Guénard G, Jombart
##   T, Larocque G, Legendre P, Madi N, Wagner HH (2022). _adespatial:
##   Multivariate Multiscale Spatial Analysis_. R package version 0.3-20,
##   <https://CRAN.R-project.org/package=adespatial>.
## 
## When using constr.hclust() please use:
## 
##   Guénard G, Legendre P (2022). "Hierarchical Clustering with
##   Contiguity Constraint in R." _Journal of Statistical Software_,
##   *103*(7), 1-26. doi:10.18637/jss.v103.i07
##   <https://doi.org/10.18637/jss.v103.i07>.
## 
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.
## 
## 
## $vegan
## 
## To cite package 'vegan' in publications use:
## 
##   Oksanen J, Simpson G, Blanchet F, Kindt R, Legendre P, Minchin P,
##   O'Hara R, Solymos P, Stevens M, Szoecs E, Wagner H, Barbour M,
##   Bedward M, Bolker B, Borcard D, Carvalho G, Chirico M, De Caceres M,
##   Durand S, Evangelista H, FitzJohn R, Friendly M, Furneaux B, Hannigan
##   G, Hill M, Lahti L, McGlinn D, Ouellette M, Ribeiro Cunha E, Smith T,
##   Stier A, Ter Braak C, Weedon J (2022). _vegan: Community Ecology
##   Package_. R package version 2.6-2,
##   <https://CRAN.R-project.org/package=vegan>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {vegan: Community Ecology Package},
##     author = {Jari Oksanen and Gavin L. Simpson and F. Guillaume Blanchet and Roeland Kindt and Pierre Legendre and Peter R. Minchin and R.B. O'Hara and Peter Solymos and M. Henry H. Stevens and Eduard Szoecs and Helene Wagner and Matt Barbour and Michael Bedward and Ben Bolker and Daniel Borcard and Gustavo Carvalho and Michael Chirico and Miquel {De Caceres} and Sebastien Durand and Heloisa Beatriz Antoniazi Evangelista and Rich FitzJohn and Michael Friendly and Brendan Furneaux and Geoffrey Hannigan and Mark O. Hill and Leo Lahti and Dan McGlinn and Marie-Helene Ouellette and Eduardo {Ribeiro Cunha} and Tyler Smith and Adrian Stier and Cajo J.F. {Ter Braak} and James Weedon},
##     year = {2022},
##     note = {R package version 2.6-2},
##     url = {https://CRAN.R-project.org/package=vegan},
##   }
## 
## 
## 
## 
## $SoDA
## 
## To cite package 'SoDA' in publications use:
## 
##   Chambers JM (2020). _SoDA: Functions and Examples for "Software for
##   Data Analysis"_. R package version 1.0-6.1,
##   <https://CRAN.R-project.org/package=SoDA>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {SoDA: Functions and Examples for "Software for Data Analysis"},
##     author = {John M Chambers},
##     year = {2020},
##     note = {R package version 1.0-6.1},
##     url = {https://CRAN.R-project.org/package=SoDA},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
## 
## 
## 
## 
## $kableExtra
## 
## To cite package 'kableExtra' in publications use:
## 
##   Zhu H (2021). _kableExtra: Construct Complex Table with 'kable' and
##   Pipe Syntax_. R package version 1.3.4,
##   <https://CRAN.R-project.org/package=kableExtra>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {kableExtra: Construct Complex Table with 'kable' and Pipe Syntax},
##     author = {Hao Zhu},
##     year = {2021},
##     note = {R package version 1.3.4},
##     url = {https://CRAN.R-project.org/package=kableExtra},
##   }
## 
## 
## 
## 
## $fuzzySim
## 
## To cite fuzzySim in publications use:
## 
##   Barbosa, A.M. (2015). fuzzySim: applying fuzzy logic to binary
##   similarity indices in ecology. Methods in Ecology and Evolution,
##   6(7), 853-858. URL
##   https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.12372.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {{fuzzySim}: applying fuzzy logic to binary similarity indices in ecology},
##     author = {A. Marcia Barbosa},
##     journal = {Methods in Ecology and Evolution},
##     year = {2015},
##     volume = {6},
##     number = {7},
##     pages = {853--858},
##     url = {https://doi.org/10.1111/2041-210X.12372},
##   }
## 
## 
## $dendextend
## 
## The methods within the package can be cited as:
## 
##   Tal Galili (2015). dendextend: an R package for visualizing,
##   adjusting, and comparing trees of hierarchical clustering.
##   Bioinformatics. DOI: 10.1093/bioinformatics/btv428
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     author = {Tal Galili},
##     title = {dendextend: an R package for visualizing, adjusting, and comparing trees of hierarchical clustering},
##     journal = {Bioinformatics},
##     year = {2015},
##     doi = {10.1093/bioinformatics/btv428},
##     url = {https://academic.oup.com/bioinformatics/article/31/22/3718/240978/dendextend-an-R-package-for-visualizing-adjusting},
##     eprint = {https://academic.oup.com/bioinformatics/article-pdf/31/22/3718/17122682/btv428.pdf},
##   }
## 
## This free open-source software implements academic research by the
## authors and co-workers. If you use it, please support the project by
## citing the appropriate journal articles.
## 
## 
## $MVPARTwrap
## 
## To cite package 'MVPARTwrap' in publications use:
## 
##   Ouellette M, Legendre. wcfP (2013). _MVPARTwrap: MVPARTwrap:
##   Additional features for package mvpart._. R package version 0.1-9.2,
##   <https://CRAN.R-project.org/package=MVPARTwrap>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {MVPARTwrap: MVPARTwrap: Additional features for package mvpart.},
##     author = {Marie-Helene Ouellette and with contributions from Pierre Legendre.},
##     year = {2013},
##     note = {R package version 0.1-9.2},
##     url = {https://CRAN.R-project.org/package=MVPARTwrap},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
## 
## 
## 
## 
## $mvpart
## 
## To cite package 'mvpart' in publications use:
## 
##   Therneau rbTM, Extensions BARporbBR<Srfv-JO<, De'ath. aortmbG (2014).
##   _mvpart: Multivariate partitioning_. R package version 1.6-2,
##   <https://CRAN.R-project.org/package=mvpart>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {mvpart: Multivariate partitioning},
##     author = {rpart by Terry M Therneau and Beth Atkinson. R port of rpart by Brian Ripley <ripley@stats.ox.ac.uk>. Some routines from vegan -- Jari Oksanen <jari.oksanen@oulu.fi> Extensions and adaptations of rpart to mvpart by Glenn De'ath.},
##     year = {2014},
##     note = {R package version 1.6-2},
##     url = {https://CRAN.R-project.org/package=mvpart},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
## 
## 
## 
## 
## $pvclust
## 
## To cite package 'pvclust' in publications use:
## 
##   Suzuki R, Terada Y, Shimodaira H (2019). _pvclust: Hierarchical
##   Clustering with P-Values via Multiscale Bootstrap Resampling_. R
##   package version 2.2-0, <https://CRAN.R-project.org/package=pvclust>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {pvclust: Hierarchical Clustering with P-Values via Multiscale Bootstrap
## Resampling},
##     author = {Ryota Suzuki and Yoshikazu Terada and Hidetoshi Shimodaira},
##     year = {2019},
##     note = {R package version 2.2-0},
##     url = {https://CRAN.R-project.org/package=pvclust},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
## 
## 
## 
## 
## $gclus
## 
## To cite package 'gclus' in publications use:
## 
##   Hurley C (2019). _gclus: Clustering Graphics_. R package version
##   1.3.2, <https://CRAN.R-project.org/package=gclus>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {gclus: Clustering Graphics},
##     author = {Catherine Hurley},
##     year = {2019},
##     note = {R package version 1.3.2},
##     url = {https://CRAN.R-project.org/package=gclus},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
## 
## 
## 
## 
## $cluster
## 
## To cite the R package 'cluster' in publications use:
## 
##   Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., Hornik,
##   K.(2022).  cluster: Cluster Analysis Basics and Extensions. R package
##   version 2.1.4.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {cluster: Cluster Analysis Basics and Extensions},
##     author = {Martin Maechler and Peter Rousseeuw and Anja Struyf and Mia Hubert and Kurt Hornik},
##     year = {2022},
##     url = {https://CRAN.R-project.org/package=cluster},
##     note = {R package version 2.1.4 --- For new features, see the 'Changelog' file (in the package source)},
##   }
## 
## 
## $ade4
## 
## To cite ade4 in publications use:
## 
##   Dray S, Dufour A (2007). "The ade4 Package: Implementing the Duality
##   Diagram for Ecologists." _Journal of Statistical Software_, *22*(4),
##   1-20. doi:10.18637/jss.v022.i04
##   <https://doi.org/10.18637/jss.v022.i04>.
## 
## Bougeard S, Dray S (2018). "Supervised Multiblock Analysis in R with
## the ade4 Package." _Journal of Statistical Software_, *86*(1), 1-17.
## doi:10.18637/jss.v086.i01 <https://doi.org/10.18637/jss.v086.i01>.
## 
## Chessel D, Dufour A, Thioulouse J (2004). "The ade4 Package - I:
## One-Table Methods." _R News_, *4*(1), 5-10.
## <https://cran.r-project.org/doc/Rnews/>.
## 
## Dray S, Dufour A, Chessel D (2007). "The ade4 Package - II: Two-Table
## and K-Table Methods." _R News_, *7*(2), 47-52.
## <https://cran.r-project.org/doc/Rnews/>.
## 
## Thioulouse J, Dray S, Dufour A, Siberchicot A, Jombart T, Pavoine S
## (2018). _Multivariate Analysis of Ecological Data with ade4_. Springer.
## doi:10.1007/978-1-4939-8850-1
## <https://doi.org/10.1007/978-1-4939-8850-1>.
## 
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.
## 
## 
## $labdsv
## 
## To cite package 'labdsv' in publications use:
## 
##   Roberts DW (2019). _labdsv: Ordination and Multivariate Analysis for
##   Ecology_. R package version 2.0-1,
##   <https://CRAN.R-project.org/package=labdsv>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {labdsv: Ordination and Multivariate Analysis for Ecology},
##     author = {David W. Roberts},
##     year = {2019},
##     note = {R package version 2.0-1},
##     url = {https://CRAN.R-project.org/package=labdsv},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
## 
## 
## 
## 
## $data.table
## 
## To cite package 'data.table' in publications use:
## 
##   Dowle M, Srinivasan A (2021). _data.table: Extension of
##   `data.frame`_. R package version 1.14.2,
##   <https://CRAN.R-project.org/package=data.table>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {data.table: Extension of `data.frame`},
##     author = {Matt Dowle and Arun Srinivasan},
##     year = {2021},
##     note = {R package version 1.14.2},
##     url = {https://CRAN.R-project.org/package=data.table},
##   }
## 
## 
## 
## 
## $pander
## 
## To cite package 'pander' in publications use:
## 
##   Daróczi G, Tsegelskyi R (2022). _pander: An R 'Pandoc' Writer_. R
##   package version 0.6.5, <https://CRAN.R-project.org/package=pander>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {pander: An R 'Pandoc' Writer},
##     author = {Gergely Daróczi and Roman Tsegelskyi},
##     year = {2022},
##     note = {R package version 0.6.5},
##     url = {https://CRAN.R-project.org/package=pander},
##   }

@article{boye-2017, author = {given-i=A., given=Aurélien, family=Boyé and given-i=P., given=Pierre, family=Legendre and given-i=J., given=Jacques, family=Grall and given-i=O., given=Olivier, family=Gauthier}, date = {2017-12}, doi = {10.1016/j.seares.2017.06.004}, journaltitle = {Journal of Sea Research}, language = {american}, pages = {107–122}, publisher = {Elsevier BV}, title = {Constancy despite variability: Local and regional macrofaunal diversity in intertidal seagrass beds}, url = {http://dx.doi.org/10.1016/j.seares.2017.06.004}, volume = {130}, } @article{boye-2019, author = {given-i=A., given=Aurélien, family=Boyé and given-i=R., given=Éric, family=Thiébaut and given-i=J., given=Jacques, family=Grall and given-i=P., given=Pierre, family=Legendre and given-i=C., given=Caroline, family=Broudin and given-i=C., given=Céline, family=Houbin and given-i=V., given=Vincent, family={Le Garrec} and given-i=M., given=Marion, family=Maguer and given-i=G., given=Gabin, family=Droual and given-i=O., given=Olivier, family=Gauthier}, date = {2019-09-18}, doi = {10.1111/ddi.12987}, journaltitle = {Diversity and Distributions}, language = {american}, number = {12}, pages = {1879–1896}, publisher = {Wiley}, title = {Trait‐based approach to monitoring marine benthic data along 500 km of coastline}, url = {http://dx.doi.org/10.1111/ddi.12987}, volume = {25}, } @article{de-caceres-2013, author = {given-i=M., given=Miquel, family={De Cáceres} and given-i=P., given=Pierre, family=Legendre and given-i=F., given=Fangliang, family=He}, date = {2013-11-18}, doi = {10.1111/2041-210x.12116}, editor = {given-i=D., given=Daniel, family=Faith}, journaltitle = {Methods in Ecology and Evolution}, language = {american}, number = {12}, pages = {1167–1177}, publisher = {Wiley}, title = {Dissimilarity measurements and the size structure of ecological communities}, url = {http://dx.doi.org/10.1111/2041-210x.12116}, volume = {4}, } @article{foubert-2017, author = {given-i=A., given=Aline, family=Foubert and given-i=F., given=Frédéric, family=Lecomte and given-i=P., given=Pierre, family=Legendre and given-i=M., given=Mathieu, family=Cusson}, date = {2017-12-06}, doi = {10.1007/s10750-017-3457-z}, journaltitle = {Hydrobiologia}, language = {american}, number = {1}, pages = {155–173}, publisher = {Springer Science and Business Media LLC}, title = {Spatial organisation of fish communities in the St. Lawrence River: a test for longitudinal gradients and spatial heterogeneities in a large river system}, url = {http://dx.doi.org/10.1007/s10750-017-3457-z}, volume = {809}, } @article{kopp-2012, author = {given-i=D., given=Dorothée, family=Kopp and given-i=Y., given=Yolande, family=Bouchon-Navaro and given-i=M., given=Max, family=Louis and given-i=P., given=Pierre, family=Legendre and given-i=C., given=Claude, family=Bouchon}, date = {2012-01}, doi = {10.2112/jcoastres-d-09-00165.1}, journaltitle = {Journal of Coastal Research}, language = {american}, pages = {63–72}, publisher = {Coastal Education and Research Foundation}, title = {Spatial and Temporal Variation in a Caribbean Herbivorous Fish Assemblage}, url = {http://dx.doi.org/10.2112/jcoastres-d-09-00165.1}, volume = {278}, } @article{lamy-2015A, author = {given-i=T., given=Thomas, family=Lamy and given-i=P., given=Pierre, family=Legendre and given-i=Y., given=Yannick, family=Chancerelle and given-i=G., given=Gilles, family=Siu and given-i=J., given=Joachim, family=Claudet}, date = {2015-09-22}, doi = {10.1371/journal.pone.0138696}, editor = {given-i={C. A.}, given={Chaolun Allen}, family=Chen}, journaltitle = {PLOS ONE}, language = {american}, number = {9}, pages = {e0138696}, publisher = {Public Library of Science (PLoS)}, title = {Understanding the Spatio-Temporal Response of Coral Reef Fish Communities to Natural Disturbances: Insights from Beta-Diversity Decomposition}, url = {http://dx.doi.org/10.1371/journal.pone.0138696}, volume = {10}, } @article{lamy-2015B, author = {given-i=T., given=Thomas, family=Lamy and given-i=P., given=Pierre, family=Legendre and given-i=Y., given=Yannick, family=Chancerelle and given-i=G., given=Gilles, family=Siu and given-i=J., given=Joachim, family=Claudet}, date = {2015-09-22}, doi = {10.1371/journal.pone.0138696}, editor = {given-i={C. A.}, given={Chaolun Allen}, family=Chen}, journaltitle = {PLOS ONE}, language = {american}, number = {9}, pages = {e0138696}, publisher = {Public Library of Science (PLoS)}, title = {Understanding the Spatio-Temporal Response of Coral Reef Fish Communities to Natural Disturbances: Insights from Beta-Diversity Decomposition}, url = {http://dx.doi.org/10.1371/journal.pone.0138696}, volume = {10}, } @article{lecchini-2003, author = {given-i=D., given=David, family=Lecchini and given-i=M., given=Mehdi, family=Adjeroud and given-i={M. S.}, given={Morgan S}, family=Pratchett and given-i=L., given=Laurence, family=Cadoret and given-i=R., given=René, family=Galzin}, date = {2003-11}, doi = {10.1016/s0399-1784(03)00048-3}, journaltitle = {Oceanologica Acta}, language = {american}, number = {5-6}, pages = {537–547}, publisher = {Elsevier BV}, title = {Spatial structure of coral reef fish communities in the Ryukyu Islands, southern Japan}, url = {http://dx.doi.org/10.1016/s0399-1784(03)00048-3}, volume = {26}, } @article{legendre-2014A, author = {given-i=P., given=Pierre, family=Legendre}, date = {2014-07-16}, doi = {10.1111/geb.12207}, journaltitle = {Global Ecology and Biogeography}, language = {american}, number = {11}, pages = {1324–1334}, publisher = {Wiley}, title = {Interpreting the replacement and richness difference components of beta diversity}, url = {http://dx.doi.org/10.1111/geb.12207}, volume = {23}, } @article{legendre-2014B, author = {given-i=P., given=Pierre, family=Legendre}, date = {2014-07-16}, doi = {10.1111/geb.12207}, journaltitle = {Global Ecology and Biogeography}, language = {american}, number = {11}, pages = {1324–1334}, publisher = {Wiley}, title = {Interpreting the replacement and richness difference components of beta diversity}, url = {http://dx.doi.org/10.1111/geb.12207}, volume = {23}, } @article{legendre-2018, author = {given-i=P., given=Pierre, family=Legendre and given-i=D., given=Daniel, family=Borcard}, date = {2018-02-23}, doi = {10.1111/ecog.03498}, journaltitle = {Ecography}, language = {american}, number = {11}, pages = {1820–1824}, publisher = {Wiley}, title = {Box-Cox-chord transformations for community composition data prior to beta diversity analysis}, url = {http://dx.doi.org/10.1111/ecog.03498}, volume = {41}, } @article{legendre-2001, author = {given-i=P., given=Pierre, family=Legendre and given-i={E. D.}, given={Eugene D.}, family=Gallagher}, date = {2001-10}, doi = {10.1007/s004420100716}, journaltitle = {Oecologia}, language = {american}, number = {2}, pages = {271–280}, publisher = {Springer Science and Business Media LLC}, title = {Ecologically meaningful transformations for ordination of species data}, url = {http://dx.doi.org/10.1007/s004420100716}, volume = {129}, } @article{legendre-1997, author = {given-i=P., given=Pierre, family=Legendre and given-i=R., given=Rene, family=Galzin and given-i={M. L.}, given={Mireille L.}, family=Harmelin-Vivien}, date = {1997-03}, doi = {10.2307/2266029}, journaltitle = {Ecology}, language = {american}, number = {2}, pages = {547}, publisher = {Wiley}, title = {Relating Behavior to Habitat: Solutions to the Fourth-corner Problem}, url = {http://dx.doi.org/10.2307/2266029}, volume = {78}, } @article{legendre-2014C, author = {given-i=P., given=Pierre, family=Legendre and given-i=O., given=Olivier, family=Gauthier}, date = {2014-03-07}, doi = {10.1098/rspb.2013.2728}, journaltitle = {Proceedings of the Royal Society B: Biological Sciences}, language = {american}, number = {1778}, pages = {20132728}, publisher = {The Royal Society}, title = {Statistical methods for temporal and space–time analysis of community composition data }, url = {http://dx.doi.org/10.1098/rspb.2013.2728}, volume = {281}, } @article{legendre-2014D, author = {given-i=P., given=Pierre, family=Legendre and given-i=O., given=Olivier, family=Gauthier}, date = {2014-03-07}, doi = {10.1098/rspb.2013.2728}, journaltitle = {Proceedings of the Royal Society B: Biological Sciences}, language = {american}, number = {1778}, pages = {20132728}, publisher = {The Royal Society}, title = {Statistical methods for temporal and space–time analysis of community composition data }, url = {http://dx.doi.org/10.1098/rspb.2013.2728}, volume = {281}, } @article{overholtzer-1999A, author = {given-i=K., given=KL, family=Overholtzer and given-i=P., given=PJ, family=Motta}, date = {1999}, doi = {10.3354/meps177177}, journaltitle = {Marine Ecology Progress Series}, language = {american}, pages = {177–187}, publisher = {Inter-Research Science Center}, title = {Comparative resource use by juvenile parrotfishes in the Florida Keys}, url = {http://dx.doi.org/10.3354/meps177177}, volume = {177}, } @article{overholtzer-1999B, author = {given-i=K., given=KL, family=Overholtzer and given-i=P., given=PJ, family=Motta}, date = {1999}, doi = {10.3354/meps177177}, journaltitle = {Marine Ecology Progress Series}, language = {american}, pages = {177–187}, publisher = {Inter-Research Science Center}, title = {Comparative resource use by juvenile parrotfishes in the Florida Keys}, url = {http://dx.doi.org/10.3354/meps177177}, volume = {177}, } @article{sharma-2012, author = {given-i=S., given=Sapna, family=Sharma and given-i=P., given=Pierre, family=Legendre and given-i=D., given=Daniel, family=Boisclair and given-i=S., given=Stéphane, family=Gauthier}, date = {2012-12}, doi = {10.1139/cjfas-2011-0505}, editor = {given-i={S. J.}, given={Stephen J.}, family=Smith}, journaltitle = {Canadian Journal of Fisheries and Aquatic Sciences}, language = {american}, number = {12}, pages = {2095–2111}, publisher = {Canadian Science Publishing}, title = {Effects of spatial scale and choice of statistical model (linear versus tree-based) on determining species–habitat relationships}, url = {http://dx.doi.org/10.1139/cjfas-2011-0505}, volume = {69}, } @article{smallhornwest-2020, author = {given-i={P. F.}, given={Patrick F.}, family=Smallhorn‐West and given-i=K., given=Karen, family=Stone and given-i={D. M.}, given={Daniela M.}, family=Ceccarelli and given-i=S., given=Siola’a, family=Malimali and given-i=T., given=Tu’ikolongahau, family=Halafihi and given-i={T. C. L.}, given={Tom C. L.}, family=Bridge and given-i={R. L.}, given={Robert L.}, family=Pressey and given-i={G. P.}, given={Geoffrey P.}, family=Jones}, date = {2020-09-02}, doi = {10.1111/conl.12755}, journaltitle = {Conservation Letters}, language = {american}, number = {6}, publisher = {Wiley}, title = {Community management yields positive impacts for coastal fisheries resources and biodiversity conservation}, url = {http://dx.doi.org/10.1111/conl.12755}, volume = {13}, }

Adjeroud, Mehdi & Briand, Marine & Kayal, Mohsen & Dumas, Pascal. (2012). Coral assemblages in Tonga: Spatial patterns, replenishment capacities, and implications for conservation strategies. Environmental monitoring and assessment. 185. 10.1007/s10661-012-2982-5. Smallhorn-West P, Gordon S, Stone K, Ceccarelli D, Malimali S, Halafihi T, et al. (2020) Biophysical and anthropogenic influences on the status of Tonga’s coral reefs and reef fish fishery. PLoS ONE 15(11): e0241146. https://doi.org/ 10.1371/journal.pone.0241146